100645 ÷ 75 
Our goal is to divide 100645 by 75.

Step 1:
When dividing 1 by 75, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 75

Going ahead to step 2:
When dividing 10 by 75, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (0) from the dividend and append it to 10, then repeat: 100 / 75

Let's proceed to step 3:
75 can be fit into 100 1 times, resulting in a remainder of 25.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 75 away from 100, we end up with 25.
Include the next digit (6) from the dividend after 25, then repeat: 256 / 75

Moving on to step 4:
75 can be fit into 256 3 times, resulting in a remainder of 31.
Put 3 as the next digit of the answer. 
Result so far: 13.0
The remainder is 31 after subtracting 225 from 256.
Grab the next digit (4) from the dividend, add it to 31, then carry on: 314 / 75

Let's proceed to step 5:
75 can be fit into 314 4 times, resulting in a remainder of 14.
Write down 4 as next digit of the result. 
Result so far: 134.0
If we subtract 300 from 314, we get 14.
Include the next digit (5) from the dividend after 14, then repeat: 145 / 75

Let's proceed to step 6:
75 goes into 145 1 times with a remainder of 70.
Write down 1 as next digit of the result. 
Result so far: 1341.0
The remainder is 70 after subtracting 75 from 145.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Step 7:
When dividing 700 by 75, we get 9 with a remainder of 25.
Record the quotient 9 as the next digit in the result. 
Result so far: 1341.9
If we subtract 675 from 700, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 8:
75 can be fit into 250 3 times, resulting in a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 1341.93
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 9:
75 goes into 250 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 1341.933
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 1341.933 with a balance of 0.0025.